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Methods of Time Discretization

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Code Completion Credits Range Language
101MTDE ZK 2 1P+1C English
Garant předmětu:
František Bubeník
František Bubeník, Petr Mayer
František Bubeník, Petr Mayer
Department of Mathematics

The course is devoted to the method highly versatile and effective for solving problems containing the time, especially evolutionary problems based on partial differential equations with various boundary and initial conditions. This method represents a modern approach to modeling and solving technical problems, both linear and non-linear, describing processes in various technical areas, such as deflections flat plates, heat conduction, vibration and others. The course contains basic concepts of functional analysis and variational methods needed to understand the formulation and modeling of technical problems, an overview of solving methods, as well as the theoretical and practical foundations. The course is conducted in an accessible form with plenty of examples.


No prerequisites are required. The course is conducted in an accessible form with many examples and does not require any special prior knowledge. Individual terms are explained from the very basics and the explanation is adapted to the students who enroll in the subject.

Syllabus of lectures:

Fundamental topics. Overview and development of computational analytical and numerical methods.

Illustrative introductory simple example, principle of time discretization. Algorithms.

Fundamental properties of function spaces.

Orthogonal and orthonormal systems.

Properties of operators.

Energy functional.

Sobolev spaces.

Classical, generalized, weak solutions.

Integral identities.

Error estimates.

Syllabus of tutorials:

The syllabus of the exercises is based on the lectures.

Study Objective:

Students are introduced to the basics necessary to understand the formulation and modeling of engineering tasks, with an overview of solution methods, as well as the practical and theoretical foundations of methods for solving time-dependent, linear and non-linear tasks.

Study materials:

Basic study materials are lectures.

Time-table for winter semester 2023/2024:
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Time-table for summer semester 2023/2024:
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The course is a part of the following study plans:
Data valid to 2024-05-25
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